标题： 最小化两次连续可微光滑强凸函数的已知最快的一阶方法 显示英文标题

标题： The Fastest Known First-Order Method for Minimizing Twice Continuously Differentiable Smooth Strongly Convex Functions

摘要： 我们研究了应用于光滑且强凸函数的迭代梯度优化算法。对于这类函数，全局收敛速度最快的算法是三重动量（Triple Momentum, TM）方法。我们证明，如果目标函数还是二阶连续可微的，则会涌现出一种新的、更快的算法，我们称之为$C^2$-动量（C2M）。我们证明了 C2M 是全局收敛的，并且其最坏情况下的收敛速率比 TM 的严格更快，且没有额外的计算成本。我们通过数值实例验证了理论发现，表明当目标函数是二阶连续可微时，C2M 的性能优于 TM。 显示英文摘要

摘要： We consider iterative gradient-based optimization algorithms applied to functions that are smooth and strongly convex. The fastest globally convergent algorithm for this class of functions is the Triple Momentum (TM) method. We show that if the objective function is also twice continuously differentiable, a new, faster algorithm emerges, which we call $C^2$-Momentum (C2M). We prove that C2M is globally convergent and that its worst-case convergence rate is strictly faster than that of TM, with no additional computational cost. We validate our theoretical findings with numerical examples, demonstrating that C2M outperforms TM when the objective function is twice continuously differentiable.